Final answer to the problem
The integral diverges.
Step-by-step Solution
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1
Since the integral $\int_{-1}^{4}4x^{-2}dx$ has a discontinuity inside the interval, we have to split it in two integrals
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$\int_{-1}^{0}4x^{-2}dx+\int_{0}^{4}4x^{-2}dx$
Learn how to solve problems step by step online. Integrate the function 4x^(-2) from -1 to 4. Since the integral \int_{-1}^{4}4x^{-2}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{-1}^{0}4x^{-2}dx results in: 4\lim_{c\to0}\left(\frac{1}{-c}-1\right). The integral \int_{0}^{4}4x^{-2}dx results in: 4\lim_{c\to0}\left(\frac{1}{-4}+\frac{1}{c}\right). Gather the results of all integrals.
Final answer to the problem
The integral diverges.
